I understand that the Mollweide projection is used to show the map of the universe. Although I understand how this projection can be interesting for Earth where most populated (and of interest) areas are not at polar latitudes, I imagine that in the sky the distribution of interesting places does not follow the same pattern of accentuating the equatorial plane.

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The equatorial plane of the Mollweide projection applied to the whole sky is usually the plane of the Milky Way. We're blatant galactic chauvinists that way.

More importantly, this projection preserves area, which is more important than angular relations for this sort of thing. For instance, when studying the CMB, in increasing level of detail, the most important questions are:

What is the overall average temperature of the CMB? (Average over area)

What direction is the overall dipole moment? (Technical way of asking which direction the Earth is moving relative to the average Universe. Easy to grasp in Mollweide. See http://aether.lbl.gov/www/projects/u2/ )

What is the size distribution of its irregularities? (In other words, how grainy is it? Area, area, area)

I think that the universe is oval since as Ernst Mach argued, the universe is ultimately sensation, specifically our visual field which in my case appears to be oval. This also explains why this insignificant life form should have a sense that can sense at the speed limit of the universe - how likely is that?! And it also explains why the universe seems to be turning out to be flat, a hologram.